Grain Risk Analysis of Meteorological Disasters in Gansu Province Using Probability Statistics and Index Approaches

Abstract

With global warming, agrometeorological disasters are also rising, posing a severe threat to China’s food security. Risk assessment serves as a bridge from disaster crisis management to risk management. Gansu Province is geographically crucial, so we performed a refined assessment of grain production risk for this province using multiple features of disaster loss data recorded at the county level. Analyses were performed for each district and county with a probability approach and an index system. We found that grain trend yields in each district and most counties in Gansu Province are increasing. Wuwei and Linxia districts had higher yearly growth rates, of more than 120 kg/(ha·year). However, there are considerable differences in risk levels among counties, even within the same district. Huating and Jinchang counties are high risk locations, while Cheng, Diebu, Jinta, and Xiahe counties are low risk zones. In 39.2% of counties, the fluctuation tendency rate of relative meteorological yield was positive. The average yield reduction rates of grain in the 1980s, 1990s, 2000s, and 2010s were 5.5%, 6.6%, 8.1%, and 4.2%, respectively, and the average fluctuation coefficients were 5.0%, 5.5%, 7.1%, and 3.8%, respectively. After 2010, most regions’ average yield reduction rates fell dramatically, and grain output progressively stabilized. Counties prone to heavy disasters are primarily spread along the Hexi Corridor, with the probability exceeding 8%. However, 27.9% of counties were spared from severe calamities, which were mainly distributed in southwestern Gansu Province. Crop disaster conditions significantly positively correlated with grain risk. Drought is the primary cause of grain yield decline in Gansu Province. The findings can provide essential policy advice for the government in disaster prevention.

1. Introduction

Agrometeorological disasters are the most common natural disasters, accounting for 70% of agricultural disasters [1]. Statistically, the area in China affected by drought, flood, hail, and other extreme events is approximately 40 million ha per year, with grain disaster losses accounting for about 10% of the overall yearly output [2]. Especially in recent years, with global warming and extreme weather events becoming more common [3], farms’ productivity has become increasingly endangered by meteorological disasters due to environmental emissions. Grain production instabilities are increasing, posing a serious challenge to farm production and food security [4,5,6].

In response to this serious issue, China has made numerous efforts to mitigate meteorological disasters. However, extensive experience has proved that we can effectively, inexpensively, and considerably minimize agricultural losses only by shifting from passive post-disaster aid to active pre-disaster risk management. Furthermore, disaster risk assessment is a bridge and an excellent tool for risk management [7]. Its goal is to identify high risk areas and implement corresponding disaster prevention measures to reduce the impact of meteorological disasters on agriculture [8]. It can assist the government in advance disaster prevention and relief actions, and is critical to the sustainable development of agriculture.

At present, there are three primary methods for assessing the risk of agrometeorological disasters: (1) index systems, (2) probability methods, and (3) scenario simulations. In index systems, the risk is determined by disaster hazard, crop exposure, and vulnerability [9], based on which index system and comprehensive risk are obtained [10,11,12,13]. This strategy is adaptable and partially explains the disaster-causing mechanism. Since the risk outcomes are too dependent on selected indicators and the assigned weights, the result is easily questioned. In the probability method, the risk is supposed to be an event space composed of (probability, loss) or (probability, event (possibility), loss). A risk assessment model is constructed by generating the probability distribution of loss [14,15]. This procedure comprises disaster loss estimation and distribution simulation steps [16]. This method has the advantages of being quantifiable, highly reliable, simple, and practicable. However, the sample size and accuracy of disaster damage data must be high. Finally, scenario simulations employ an agricultural model to replicate the process of disaster impact on agriculture and assess the agricultural output risk under various disaster scenarios. This method can reflect the feedback mechanism among the elements of the disaster system, but is difficult to realize due to the complexities of the model structure and the inaccessibility of model parameters. Therefore, this strategy is only appropriate for small research regions with homogeneous land surfaces and similar climatic conditions [17].

Currently, many types of research on meteorological disaster risks are being conducted worldwide. For example, Hoque et al. [10], Pei et al. [18], Meza et al. [12], and Carrao et al. [14] assessed the agricultural drought risk in different regions of the world based on disaster hazard, crop exposure and vulnerability, and disaster resistance capabilities. Hagenlocher et al. [11] summarized the progress of drought-disaster vulnerability and risk assessment. These studies mainly employed the index technique and were directed at particular disasters. Additionally, some researchers undertook agricultural production risk evaluations using scenario analysis approaches. For example, Zhu et al. [19], Yin et al. [20], and Wang et al. [21] estimated the comprehensive risk of drought disasters in different countries using various crop models. Rosenzweig et al. [22] evaluated the worldwide production risk of four crops under different climate scenarios based on multiple climate and crop growth models. Hirabayashi et al. [23] assessed the worldwide flood disaster risk using multiple climate models and concluded that climate change would substantially raise the regional flood disaster risk. Furthermore, other researchers conducted meteorological disaster risk assessments using loss data and probability approaches. For instance, Deng et al. [24], Han et al. [25], Guo et al. [26], and Wu et al. [27] established a comprehensive meteorological disaster risk index based on yield loss data and separately obtained rice risk zoning maps in various provinces of China. Qian et al. [28] assessed the global food production risk based on only yield reduction information. Most studies were aimed at a specific crop in a particular area, and there are few studies on food production risk assessments in the Gansu Province of China.

To summarize, probability techniques quantify the comprehensive effects of multi-disasters and have been widely accepted as an efficient and convenient risk assessment indicator [29]. The index system approach is influenced by the indicator choice and its weight, but it is flexible. The simulation approach has the disadvantage of being generally inappropriate for large-scale studies. Therefore, we used a probability and index system approach to measure the meteorological disaster risk in this study.

Moreover, the previous studies based on the probability method also have some limitations. First, most prior risk analyses have been concentrated in economically developed southern China, and paid little attention to the crop production of Gansu Province. Second, agricultural risks were mainly evaluated at the provincial or district level [30]. The geospatial resolution was coarse, meaning they struggled to meet farmers’ needs for field management, and was also unfavorable as the government attempted to formulate targeted disaster prevention measures. Third, most researchers regarded risk as static, only obtaining a region’s overall risk background. They did not consider that the risk was also changing and had new characteristics. Four, most studies only produce risk assessment results and rarely verify the reliability of the results.

Gansu Province connects the west and east of China, and its geographical location is critical. Agriculture is the leading industry. Wheat, corn, and potato are the principal grain crops. However, there are currently few studies on the risk of grain production in this province. Therefore, refined risk assessments of grain production in this province are meaningful and urgent.

The objective of this study is to present a comprehensive assessment framework of grain production risk based on multiple features of disaster loss data and by combining the probability with the index technique. Next, the grain production risk at the county level in Gansu Province was estimated, and the new characteristics of the spatiotemporal variations of risk were also presented. Furthermore, the verification of risk results was also explored. Through these analyses, we can identify high risk counties of food production and clarify the characteristics of risk variations. The outcomes will provide a decision-making basis and scientific reference for the government to deal with climate change, reduce meteorological disaster risk, and stabilize agricultural production.

This paper is organized as follows. The regional characteristics and required data are briefly introduced in the Study Area and Data Sources sections. The overall framework and method of risk analysis are described in detail in the Methodology section. The findings of this study and analysis are presented in the Results section. Finally, the suggested lines for further research and primary outcomes are summarized in the Discussion and Conclusion sections.

2. Study Area

Gansu Province, with an area of 45.4 × 10⁴ km², is located in the arid and semiarid regions of Northwest China, near the upper reaches of the Yellow River, just at the intersection of Qinghai Tibet, Inner Mongolia, and the Loess Plateau. The terrain is long and narrow, measuring 1655 km from east to west and 530 km from south to north, and it is 618~5482 m above sea level. The landscape slopes from southwest to northeast and is highly vulnerable across mountains, plateaus, plains, valleys, deserts, and the Gobi. The province is divided into six regions: the South Mountains, the east rain-fed agriculture, the middle Loess Plateau, the Gannan Plateau, the Qilian Mountains, and the Hexi Corridor. The climate is complicated and varied, ranging from dry regions to humid subtropical areas. The average annual temperature is 0~14 °C, the yearly sunlight hours are 1700~3300 h, and the annual average precipitation is 42~760 mm. Meteorological disasters frequently occur, accounting for 88.5% of natural disasters, which is greater than the national average and has severely impacted agriculture [30].

The sown area of grain crops is 2.6 × 10⁶ ha, accounting for 67.2% of the total crop-planting area. The grain crops comprise three types, namely, cereal, soybeans, and tubers. Wheat, corn, and potato are the three main grain crops in Gansu Province, accounting for 86.6% of the total grain crop area.

Gansu Province administers fourteen districts, including Lanzhou, Jiayuguan, Jinchang, Baiyin, Tianshui, Wuwei, Zhangye, Pingliang, Jiuquan, Qingyang, Dingxi, Longnan, Linxia, and Gannan. These fourteen districts control 86 counties. The administrative map is displayed in Figure 1.

3. Data Sources

Each county used three types of data: grain yield, disaster, and cultivation information. Disaster information refers to crops’ total-affected and total-disaster areas from 1984 to 2020, as well as the crop’s drought-affected (1984–2020) and drought-disaster (1991–2020) areas. The sown areas of crop and grain from 1984 to 2020 were included in the cultivation statistics.

Among them, the total-affected and total-disaster areas of crops refer to the crop-sown areas with yield reductions of more than 10% and 30% due to disasters, respectively. The crop’s drought-affected and drought-disaster areas represent the crop-sown areas whose yields were reduced by more than 10% and 30% due to drought, respectively.

Data were gathered from the Gansu Statistical Yearbook (1984–2020), the Gansu Rural Economic Yearbook (1992–1999), and the Gansu Rural Yearbook (2000–2020). The accurate grain yield data for each county in Gansu Province from 1984 to 2020 were obtained by comparing and verifying various data sources.

4. Methodology

The grain trend yield was estimated using the moving average method and historical yield data from each county in Gansu Province. The meteorological yield and relative meteorological yield were calculated on this basis. Then, various risk indicators (such as the average yield reduction rate, maximum yield reduction rate, average fluctuation coefficient, fluctuation tendency rate, the variation coefficient of yield reduction, and probability of different yield reduction rates) were obtained and used to build a comprehensive risk evaluation index system. Finally, the meteorological disaster risk of grain in Gansu Province was thoroughly and objectively assessed. Furthermore, the relationship between risk zoning and disaster information was examined to validate the risk results. The technical framework is depicted in Figure 2.

4.1. Yield Detrending

Grain yield can be divided into two components: trend yield and meteorological yield [31,32].

$$Y=Y_t+Y_w$$

(1)

$$Y_r=\frac{Y_w}{Y_t}\times 100\%$$

(2)

Here, $Y$ is the grain yield per unit area; $Y_t$ is the trend yield, which is determined for the development of the social economy, science, and technology; $Y_w$ is the meteorological yield affected by weather factors; and $Y_r$ is the relative meteorological yield, which reflects the intensity of the impact of meteorological factors on the yield.

4.2. Risk Indicator Calculation

4.2.1. Average Yield Reduction Rate

The average yield reduction rate shows the entire condition of grain yield decline [25], namely,

$$AR=\frac{1}{n}{\displaystyle \sum _{i=1}^n{Y}_{r_i}}\hspace{1em}\hspace{1em}(Y_{r_i}<0)$$

(3)

In this equation, AR is the average yield reduction rate, $Y_{r_i}$ is the negative $Y_r$, and n is the number of yield reduction years. Furthermore, the average yield reduction rates from 1984 to 1990, 1991 to 2000, 2001 to 2010, and 2011 to 2020 are used to determine the interdecadal values in the 1980s, 1990s, 2000s, and 2010s, respectively.

4.2.2. Maximum Yield Reduction Rate

The maximum yield reduction rate reflects the catastrophic loss of crop throughout time and is calculated as follows:

$$MR=\min (Y_r)$$

(4)

where MR denotes the maximum yield reduction rate, and $Y_r$ is the relative meteorological yield sequence.

4.2.3. Average Fluctuation Coefficient

The average fluctuation coefficient refers to the average situation of yield instability.

$$BR=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|Y_{r_i}\right|}$$

(5)

where BR represents the average fluctuation coefficient, $Y_{r_i}$ is the relative meteorological yield in the ith year, and n represents the year sequence. Simultaneously, the interdecadal values of the average fluctuation coefficient were computed.

4.2.4. Fluctuation Tendency Rate

The yield instability trend is indicated by the fluctuation tendency rate, which can be extracted from the linear regression equation of fluctuation coefficient against time, and the slope represents the tendency rate.

$$B{R}_s=regressio{n}_{line}(\left|Y_r\right|,year)$$

(6)

where $B{R}_s$ is the fluctuation tendency rate and $Y_r$ represents the relative meteorological yield sequence.

4.2.5. Trend Yield Tendency Rate

The trend yield tendency rate can be obtained from the linear regression equation of trend yield against time, as follows:

$$Y_{ts}=regressio{n}_{line}(\left|Y_t\right|,year)$$

(7)

Here $Y_{ts}$ is the trend yield tendency rate and $Y_t$ represents the trend yield sequence.

4.2.6. Coefficient of Yield Variation

The coefficient of yield variation reflects the degree of yield dispersion and is the ratio of standard deviation to the average of actual yield [32]. The greater the variation coefficient is, the greater the yield fluctuation.

$$C{V}_Y=\frac{\sqrt{{\displaystyle \sum _{i=1}^n{(Y_i-\overline{Y})}^2/(n-1)}}}{\overline{Y}}$$

(8)

Here, $C{V}_Y$ is the coefficient of yield variation, $Y_i$ is the yield in the ith year, $\overline{Y}$ is the average yield, and n is the year series.

4.2.7. Coefficient of Variation of Yield Reduction Rate

The coefficient of variation of the yield reduction rate represents the degree of dispersion of the yield reduction rate [28]. The smaller the coefficient of variation of yield reduction rate, the higher the probability of various degrees of disaster.

$$C{V}_{YR}=\frac{\sqrt{{\displaystyle \sum _{i=1}^n{(Y_{r_i}-AR)}^2/(n-1)}}}{AR}(Y_{r_i}<0)$$

(9)

Here, $C{V}_{YR}$ is the coefficient of variation of yield reduction rate, $Y_{r_i}$ is the negative $Y_r$, AR is the average yield reduction rate, and n is the number of yield reduction years.

4.2.8. Probability of Different Yield Reduction Rates

The meteorological disasters corresponding to different yield reduction rates are obviously different. Therefore, it is of great significance to determine the probability of different yield reduction rates for assessing the risk of meteorological disasters.

$$P(Y_{r1}<Y_r\le Y_{r2})={\displaystyle {\int }_{Y_{r_1}}^{Y_{r_2}}f(Y_r})dx$$

(10)

Here, $P(Y_{r1}<Y_r<Y_{r2})$ is the probability of a yield reduction rate within the $(Y_{r1},Y_{r2}]$ interval, $Y_r$ is the relative meteorological yield, and $f(Y_r)$ is the probability of a particular yield reduction rate [25,28]. P_[−5%,0], P_{[−10%,−5%)}, P_{[−20%,−10%)}, P_{[−30%,−20%)}, and P_(<−30%) represent the probabilities of yield reduction rates at (−5%,0], (−10%, −5%], (−20%, −10%], and (−30%, −20%] intervals, and less than −30%, respectively.

For each risk index, the percentile technique was used for dividing into five levels: low (0, 20%], medium–low (20%, 40%], medium (40%, 60%], medium–high (60%, 80%], and high (80%, 100%]. For classifying interdecadal evolution, the equal interval plus percentile technique was utilized. The spatial distribution maps were drawn using Arcgis10.0 software.

4.3. Risk Indicator Normalization and Comprehensive Risk Level

4.3.1. Normalization of Risk Indicators

Due to the unit and absolute value disparities among risk indicators, normalization was required for each indicator. The deviation standardization approach was used in this case [12,14].

$$Z_i=\{\begin{array}{l}\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}\begin{array}{ccccc}& & & & \end{array} (\mathrm{positive} \mathrm{normalization} )\\ 1-\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}\begin{array}{cccc}& & & \end{array}(\mathrm{negative} \mathrm{normalization} )\end{array}$$

(11)

Here $x_i$ is the original data; $x_{\max }$ and $x_{\min }$ indicate the maximum and minimum values of the $x_i$ sequence, respectively; and $Z_i$ is the normalized data with a value range of [0, 1.0]. When $Z_i$ was 1.0, the risk was greatest; when $Z_i$ was 0, the risk was lowest. If $Z_i$ varied from 0 to 1.0 as $x_i$ increased, the positive normalized calculation formula was used; otherwise, the negative standardized calculation formula was used.

In this study, negative normalization was used to calculate $Y_{ts}$, AR, MR, $C{V}_{YR}$, P_[−5%,0], P_{[−10%,−5%)}, and four decadal AR values (1980s, 1990s, 2000s, and 2010s), while BR_s, BR, CV_Y, P_(<−30%), and four decadal BR values (1980s, 1990s, 2000s, and 2010s) were computed using positive normalization.

4.3.2. Comprehensive Risk Level

According to the index characteristics, eighteen indicators, including $Y_{ts}$, AR, MR, $C{V}_{YR}$, BR_s, BR, CV_Y, P_[−5%,0], P_{[−10%,−5%)}, P_(<−30%), as well as four decadal AR and BR values, were chosen.

Following normalization, the weighted average value of the above eighteen indicators was used to calculate the comprehensive risk level of each county:

$$R={\displaystyle \sum _{i=1}^n(ris{k}_{index,}{}_i\times W_i)}$$

(12)

Here, $R$ is the comprehensive risk level, ${risk}_{index,i}$ and $W_i$ are the risk level and weight of the ith indicator, and n is the indicator number. Equal weight (1/18) was adopted.

4.3.3. Risk Classification

The comprehensive risk was classified into five levels: high, medium–high, medium, medium–low, and low. The standard deviation technique and the K-means clustering algorithm were used for risk classification.

Regarding the standard deviation method, the classification criteria used for each risk level are presented in

Table 1. The standard deviation classification method.

The Value Range of the Risk Index	Risk Region
[μ + 1.5σ, 1]	High risk
[μ + 0.5σ, μ + 1.5σ]	Medium–high risk
[μ − 0.5σ, μ + 0.5σ]	Medium risk
[μ − 1.5σ, μ − 0.5σ]	Medium–low risk
[0, μ − 1.5σ]	Low risk

Note: μ is the mean value of the risk index; σ is the standard deviation of the risk index.

.

The K-means clustering approach relies on division and iterative solutions [33]. The data were divided into K clusters, and the points within each cluster were as close as possible, while the distance between clusters was as great as possible. The primary input parameters were the number of classification categories (K) and the maximum number of iterations (T). This algorithm was implemented in MATLAB software.

4.4. Verification of Risk Outcomes

Total-affected rate ($Rati{o}_{tsz}$):

$$Rati{o}_{tsz}=\frac{Are{a}_{sz}}{SOWNare{a}_{crop}}$$

(13)

Total-disaster rate ($Rati{o}_{tcz}$):

$$Rati{o}_{tcz}=\frac{Are{a}_{cz}}{SOWNare{a}_{crop}}$$

(14)

Drought-affected rate ($Rati{o}_{ghsz}$):

$$Rati{o}_{ghsz}=\frac{Are{a}_{ghsz}}{SOWNare{a}_{crop}}$$

(15)

Drought-disaster rate ($Rati{o}_{ghcz}$):

$$Rati{o}_{ghcz}=\frac{Are{a}_{ghcz}}{SOWNare{a}_{crop}}$$

(16)

Grain affected area ($Grainare{a}_{tsz}$):

$$Grainare{a}_{tsz}=Rati{o}_{tsz}\times SOWNare{a}_{grain}$$

(17)

Grain disaster area ($Grainare{a}_{tcz}$):

$$Grainare{a}_{tcz}=Rati{o}_{tcz}\times SOWNare{a}_{grain}$$

(18)

Grain drought-affected area ($Grainare{a}_{ghsz}$):

$$Grainare{a}_{ghsz}=Rati{o}_{ghsz}\times SOWNare{a}_{grain}$$

(19)

Grain drought-disaster areas ($Grainare{a}_{ghcz}$):

$$Grainare{a}_{ghcz}=Rati{o}_{ghcz}\times SOWNare{a}_{grain}$$

(20)

Here, $Are{a}_{sz}$, $Are{a}_{cz}$, $Are{a}_{ghsz}$, and $Are{a}_{ghcz}$, respectively, denote the total-affected and total-disaster area, and the drought-affected and drought-disaster area. $SOWNare{a}_{crop}$ and $SOWNare{a}_{grain}$ are the sown areas of crops and grains, respectively.

The multi-year average of disaster data was used to validate the reliability of risk outcomes.

First, the total-affected and total-disaster rates were individually calculated based on the crop disaster data. Next, the affected and disaster areas of grain were separately determined based on the grain-planted area. Then, utilizing drought-disaster data, the effect of drought on grain production risk was briefly assessed.

The verification was performed by examining the correlation between each risk variable and the disaster information. Normalized risk indicators were adopted for ease of use; here, the higher the value, the greater the risk. First, all disaster information and risk indicators were subjected to normal distribution tests. The tests found that numerous variable sequences had non-normal distributions; thus, the Spearman correlation coefficient was selected.

Furthermore, the significance test results of the correlation coefficients required various corrections because the multiple correlation analyses (eighteen risk indicators, one risk level, and twelve points of disaster information) between risk variables and disaster information involved multiple comparisons and tests. The Bonferroni correction method is now the simplest and most commonly used [34]. The procedure was carried out by correcting the p-value of the significance test, with the significance level set to 0.05, and then dividing the p-value by the number of hypothesis tests (i.e., 0.05/((18 + 1) × 12) = 0.0002) [35]. A correlation may be deemed significant after the Bonferroni correction if its p-value remains less than the adjusted p-value (p < 0.0002). We computed the p-value and also marked the significance after Bonferroni correction. The statistical analysis was completed by the Statistical Package for Social Sciences (SPSS 16.0) for Windows.

5. Results

5.1. Grain Production Risk Assessment for the Districts of Gansu Province

5.1.1. Variations of Grain Trend Yield in Gansu Province Districts

The trend yields of all districts are increasing, implying that scientific and technological advancement is considerably promoting grain production there (Figure 3). The maximum trend yields of Jiayuguan and Jiuquan districts were higher, reaching 9743 kg/ha and 9499 kg/ha, respectively. However, the maximum and average trend yields of Gannan District are the lowest, at 2550 kg/ha and 2120 kg/ha, respectively.

Moreover, Wuwei and Linxia districts have the highest grain yield increase rates, reaching 124.5 kg/(ha·year) and 125.4 kg/(ha·year), respectively. Gannan and Zhangye had the lowest grain yield increase rates, with 32.6 kg/(ha·year) and 52.6 kg/(ha·year), respectively. There are nine districts with annual grain yield increases exceeding 75 kg/(ha·year).

5.1.2. Variations of Grain Relative Meteorological Yield in Gansu Province Districts

The grain relative meteorological yields in districts of Gansu Province change primarily around 20% (Figure 4). The proportions with fluctuations within the intervals of [0, ±5%), [±5%, ±10%), [±10%, ±20%), and [±20%, ±30%), and above ±30%, are 63.5%, 21.1%, 11.2%, 3.3%, and 1.0%, respectively. These vary greatly in Jiayuguan, Jinchang, Tianshui, and Qingyang districts.

5.1.3. Grain Production Risk in Gansu Province Districts

In addition, some risk indicators, such as the average yield reduction rate and its variation coefficient, can quantify the detailed influence of meteorological elements on yield (

Table 2. Risk characteristics of grain production in the districts of Gansu Province.

District	Relative Meteorological Yield (Yr)					Yield (Y)	Average Yield Reduction Rate (AR, %)				Average Fluctuation Coefficient (BR, %)
	AR (%)	MR (%)	BR (%)	BRs (%/Year)	CVYR	CVY	1980s	1990s	2000s	2010s	1980s	1990s	2000s	2010s
Lanzhou	−7.16	−16.44	5.88	0.06	−0.76	0.31	−5.77	−11.31	−7.07	−5.84	5.00	7.41	4.25	6.61
Jiayuguan	−8.55	−43.01	7.43	0.34	−1.45	0.19	−1.60	−3.14	−20.22	−9.61	2.17	2.54	15.12	8.30
Jinchang	−9.37	−37.39	8.16	−0.13	−1.32	0.23	−9.68	−2.87	−17.48	−4.75	11.96	3.03	16.31	2.48
Baiyin	−3.80	−22.57	4.02	0.04	−1.72	0.31	−4.12	−0.76	−11.63	−2.13	3.85	1.27	8.86	2.04
Tianshui	−5.52	−38.90	5.47	−0.15	−1.61	0.34	−6.03	−9.91	−3.08	−2.40	4.84	10.60	3.90	2.35
Wuwei	−6.56	−13.89	5.40	0.10	−0.65	0.30	−5.55	−8.29	−8.59	−3.30	2.15	4.49	9.94	4.04
Zhangye	−3.13	−8.02	3.16	0.06	−0.71	0.14	−1.61	−2.35	−4.50	−3.03	1.66	2.39	5.29	2.85
Pingliang	−7.47	−29.02	7.03	−0.03	−1.02	0.34	−8.58	−10.67	−4.65	−6.41	6.88	9.58	5.33	6.30
Jiuquan	−3.61	−11.51	2.98	0.11	−0.94	0.19	−1.84	−1.81	−4.76	−5.87	1.56	1.71	4.49	3.75
Qingyang	−11.58	−26.08	8.46	−0.23	−0.70	0.32	−12.10	−14.36	−16.25	−4.90	10.66	10.19	10.22	3.44
Dingxi	−4.93	−25.28	5.17	−0.15	−1.12	0.34	−4.31	−8.83	−2.57	−4.01	5.58	8.51	2.97	3.73
Longnan	−5.42	−21.01	4.70	−0.06	−1.00	0.26	−5.32	−5.50	−7.86	−2.35	5.36	3.91	7.54	2.19
Linxia	−4.68	−20.86	4.38	−0.07	−1.06	0.32	−3.93	−8.30	−3.50	−2.45	3.28	7.67	3.42	2.83
Gannan	−2.82	−9.84	2.98	−0.09	−1.00	0.18	−5.81	−4.15	−1.12	−2.15	5.00	3.77	1.13	2.63
Average							−5.45	−6.59	−8.09	−4.23	5.00	5.51	7.05	3.82

).

Except for Qingyang, the average yield reduction rate is less than 10% in most districts. Second, the Lanzhou, Jiayuguan, Jinchang, and Pingliang districts have relatively high average yield reduction rates (AR < −7%), indicating that meteorological disasters have substantially impacted their grain yield for a long time.

The maximum yield reduction rate reflects huge historical losses related to severe or catastrophic events. Food production in Jiayuguan, Jinchang, and Tianshui has been devastated by natural disasters (MR < −30%), while no severe disaster has occurred in Zhangye or Gannan (MR > −10%). This loss exceeded 20% in nine districts, showing that weather disasters caused considerable grain losses in most of Gansu Province.

The average fluctuation coefficient of the districts varies from 2.98% to 8.46%. It has changed dramatically in Jiayuguan, Jinchang, Pingliang, and Qingyang districts, indicating that meteorological elements have major effects on their yields. However, these values in the Gannan and Jiuquan districts are comparatively low (BR < 3%).

The fluctuation tendency rate changes from −0.23%/year to 0.34%/year, with most districts differing by 0.2%/year. Eight districts have negative results, showing that the influence of climatic conditions on yield has gradually decreased. In particular, it is lowest in Qingyang (−0.23%/year), but the other six districts have a positive tendency rate, especially in Jiayuguan (0.34%/year).

The yield variation coefficient ranges from 0.14 to 0.34. Eight districts have values greater than 0.3, showing that the interannual fluctuations of grain yield are large. However, those in Jiayuguan, Zhangye, and Gannan districts are small (CV_Y < 0.2).

The variation coefficient of yield reduction rate differs from −1.72 to −0.65 across the districts. In Jiayuguan, Jinchang, Baiyin, and Tianshui, it is lower than in other districts, where the yield reduction rates change dramatically, and there are numerous slight and severe disasters. However, those of Lanzhou, Wuwei, Zhangye, and Qingyang are higher, suggesting that the meteorological disaster loss rate has mostly stayed the same for a long time.

In general, the average yield reduction rate and fluctuation coefficient of Jiayuguan, Jinchang, Pingliang, and Qingyang districts are considerably higher than those of other regions, and meteorological disasters greatly harm these areas.

Furthermore, decadal variations in yield reduction rate and fluctuation coefficient are here investigated (Table 2).

The average yield reduction rates and average fluctuation coefficients of Lanzhou, Tianshui, Pingliang, Dingxi, and Linxia fell considerably after 2000, while those of Jiayuguan, Jinchang, Baiyin, Wuwei, Qingyang, and Longnan decreased dramatically after 2010. For the whole of Gansu Province, in the 1980s, 1990s, 2000s, and 2010s, the yield reduction rates were 5.45%, 6.59%, 8.09%, and 4.23%, respectively, and the fluctuation coefficients were 5.00%, 5.51%, 7.05%, and 3.82%, respectively. Apparently, the grain yield fluctuations in Gansu Province were still severe, and the yield reduction rate was considerable during the 2000s, but they decreased dramatically within the last ten years.

5.1.4. Probability of Different Yield Reduction Rates in Gansu Province Districts

The probability of different yield reduction rates in Gansu Province districts is here examined (Figure 5). The probability of slight disaster loss, with a yield reduction rate of less than 5%, is greater in Baiyin, Zhangye, and Gannan districts. The Wuwei and Dingxi districts have higher yield reduction rates at (−10%, −5%] intervals. Furthermore, Lanzhou, Wuwei, Pingliang, and Qingyang are more likely to experience a 10–20% rate of decrease, while Baiyin and Qingyang are more likely to experience a 20–30% reduction rate. In addition, the probability of severe disasters (more than 30%) is higher in Jiayuguan, Jinchang, and Tianshui districts, and the remaining districts are free of severe disasters.

5.2. Risk Assessment of Grain Production in Gansu Province Counties

5.2.1. Variations of Grain Trend Yield in Gansu Province Counties

The interdecadal variations of grain trend yield in the counties of Gansu Province are depicted in Figure 6.

In the 1980s, trend yields were below 3000 kg/ha in 77.2% of counties, primarily to the south of Wuwei District. In addition, 15.2% and 7.6% of counties had trend yields of more than 4500 kg/ha and 6000 kg/ha, respectively, primarily dispersed in Zhangye, Jiuquan, and Jiayuguan districts.

The trend yield increased dramatically during the 1990s. It rose to more than 1500 kg/ha in most counties to the south of Wuwei District and more than 6000 kg/ha in most counties to the west. The proportion of counties below 3000 kg/ha fell to 68.4%. The proportions of counties with trend yields greater than 4500 kg/ha, 6000 kg/ha, and 7500 kg/ha are 21.5%, 15.2%, and 8.9%, respectively, remaining scattered along the Hexi Corridor.

This changed little in the regions to the south of Wuwei over the 2000s, but increased dramatically in most counties to the west of Wuwei, exceeding 9000 kg/ha in several counties. The proportion of counties with a trend yield below 3000 kg/ha decreased to 50.6%. The proportions of counties exceeding 4500 kg/ha, 6000 kg/ha, and 7500 kg/ha are 27.9%, 19.0%, and 13.9%, respectively, with Dunhuang County having the highest value.

After 2010, the trend yields of most counties to the south of Wuwei climbed to more than 3000 kg/ha, but those to the west of Wuwei showed little change or even a decline. Only 17.7% of counties have a trend yield of less than 3000 kg/ha, while the proportions of counties with a trend yield above 4500 kg/ha, 6000 kg/ha, and 7500 kg/ha increased to 40.5%, 26.6%, and 15.2%, respectively.

The tendency rate of the trend yield variation is depicted in Figure 7. The trend yields in most counties are rising. The proportions of counties with annual trend yield increases between 0 and 30 kg/(ha·year), 30 and 60 kg/(ha·year), 60 and 90 kg/(ha·year), and 90 and 120 kg/(ha·year), and greater than 120 kg/(ha·year), are 5.2%, 20.8%, 45.5%, 14.3%, and 14.3%, respectively. The annual trend yield increase is less than 90 kg/(ha·year) in most counties to the south of Wuwei and even below 30 kg/(ha·year) in the Gannan region. However, the increase is clear in the counties to the west of Wuwei (Y_ts > 90 kg/(ha·year)), and is even more than 120 kg/(ha·year) in several counties, where social and economic development has greatly aided the increase in grain yield. In addition, it is negative in the Gaotai and Linze counties, mainly because their trend yields were historically consistently high but somewhat declined after 2010.

5.2.2. Grain Production Risk in Gansu Province Counties

Figure 8a depicts the average grain yield reduction rates of counties in Gansu Province. The areas with a high average yield reduction rate (AR < −12.8%) are concentrated in the Middle East of Gansu Province, including Jinchang, Yongchang, Huining, Jingtai, Zhangjiachuan, Gulang, Huating, Jingning, Akesai, Xifeng, Qingcheng, Huan, Zhengning, Liangdang, Yongjing, and Jishishan counties.

Extreme meteorological disasters have occurred in Jinchang, Yongchang, Baiyin, Huining, Jingtai, Gangu, Zhangjiachuan, Minqin, Gulang, Gaotai, Huating, Qingcheng, Zhengning, Hui, Liangdang, and Hezheng counties (MR < −47.0%) (Figure 8b). However, there has been no severe yield loss in some counties.

The average fluctuation coefficient is shown in Figure 8c. Jinchang, Yongchang, Huining, Zhangjiachuan, Gulang, Lingtai, Huating, Jingning, Aksai, Qingcheng, Huanxian, Ning, Zhenyuan, Yongjing, and Jishishan counties show strong yield fluctuations (BR > 11.3%).

Figure 8d displays the fluctuation tendency rate of the relative meteorological yield. In total, 39.2% of counties show a positive fluctuation tendency, mainly concentrating in the central and western Gansu Province, which indicate that weather conditions had an increasing impact on grain output in these counties. However, it was less than −0.25%/year in 20.3% of counties, so their grain productions gradually tended towards stability.

Figure 8e depicts the yield variation coefficients. Counties with large variation coefficients are primarily found in Gansu Province’s central region, including Jinchang, Huining, Zhangjiachuan, Gulang, Lingtai, Huating, Qingcheng, Huanxian, Zhenyuan, Anding, Tongwei, Dangchang, and Yongjing (CV_Y > 0.41). Nevertheless, this rate is less than 0.23 in some counties, where grain yield is relatively steady.

Moreover, regions with a greater dispersion degree of the yield reduction rate are primarily located in eastern Gansu, including Jingyuan, Jingtai, Qinzhou, Qin’an, Qingshui, Zhangjiachuan, Jiayuguan, Baiyin, Minqin, Gaotai, Jingchuan, Zhengning, Hui, Liangdang, and Linxia counties (CV_YR < −1.42) (Figure 8f). In contrast, it is in the range of [−0.86,0] in some counties, where the meteorological disaster loss has mostly stayed the same over time.

5.2.3. Spatiotemporal Variation of Grain Production Risk in Gansu Province Counties

Temporal Evolution of the Average Yield Reduction Rate in Gansu Province Counties

Figure 9 depicts the spatiotemporal variations of the average grain yield reduction rate in Gansu Province’s counties.

In the 1980s, the proportions of counties with average yield reduction rates of [0, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] intervals were 15.2%, 20.3%, 24.1%, and 34.2%, respectively (Figure 9a). Jinchang county is the highest (AR = 47.2%), followed by Yongchang, Qingcheng, Huan, and Guanghe (AR > 20%). However, these values in the Hexi Corridor and southern Gansu regions are low, and are less than 3% in twelve counties. In brief, areas with severe yield reductions were primarily spread south of Jinchang during this period.

In the 1990s, the average yield reduction rates increased in certain areas, such as Zhangye District, while they decreased in some regions, including Longnan and Jiuquan districts (Figure 9b). In most counties, it was less than 20%. The proportions of counties with average yield reduction rates of [0, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] are 11.4%, 10.1%, 29.1%, and 46.8%, respectively. The rate is less than 3% in nine counties and more than 20% only in Jinchang and Akesai counties. Compared to the 1980s, the proportion of counties in the [5%, 20%) interval increased. Furthermore, it grew in 57.0% of counties, and Gangu, Zhangjiachuan, Tianzhu, Akesai, and Longxi counties increased by more than 10%. During this period, the areas showing severe yield loss remained to the south of Jinchang, and the spatial distributions of the heavy and light disaster zones changed little.

In the 2000s, the average yield reduction rate increased dramatically, and that of most counties was more than 10% (Figure 9c). The proportions of counties with average yield reduction rates of [0, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] are 8.9%, 5.1%, 21.5%, and 26.6%, respectively. Nine counties have shown higher average yield reduction rates (more than 30%), while the yield reduction is less than 3% in seven counties. Compared to the 1990s, the yield reduction rate has increased in 64.6% of counties, and Jingtai, Zhengning, Liangdang, and Luqu increased by more than 30%. The serious disaster loss regions expanded dramatically. Furthermore, the disaster loss in central and western Gansu was slight before 2000 but serious after that year. However, in southern Gansu, the average yield reduction rate decreased after 2000. During this period, the severe disaster zone was altered dramatically.

The disaster loss in most counties has dramatically improved since 2010 (Figure 9d). The proportions of counties with average yield reduction rates of [0, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] are 39.2%, 27.9%, 27.9%, and 3.8%, respectively, and the proportion of lightly affected counties has increased dramatically. In total, 87.34% of counties showed decreases, and eight counties had a decrease of more than 30%.

Temporal Evolution of the Average Fluctuation Coefficient in Gansu Province Counties

The average fluctuation coefficient of grain relative meteorological yield in counties of Gansu Province is shown in Figure 10.

In the 1980s, the proportions of counties with average fluctuation coefficients of [0, 2%], (2%, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] were 3.8%, 11.4%, 22.8%, 37.9%, and 21.6%, respectively (Figure 10a). Jinchang and Yongchang had the most fluctuations (BR > 20.0%), while the fluctuation ranges of Minqin, Ganzhou, and Jinta counties were less than 2.0%.

In the 1990s, the proportions of counties with average fluctuation coefficients of [0, 2%], (2%, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] were 2.5%, 10.2%, 12.6%, 34.2%, and 36.7%, respectively (Figure 10b). The percentage of counties between 10% and 20% increased dramatically. The areas with severe fluctuations were found in Jinchang, Dongxiang, and Jishishan counties (BR > 20%), while small fluctuations were found in Ganzhou and Linxia counties (BR < 2%). The average fluctuation coefficient of 57.0% of counties increased dramatically.

The grain relative meteorological yield changed more strongly in the 2000s, and most counties’ average fluctuation coefficients exceeded 10% (Figure 10c). The proportions of counties with an average fluctuation coefficient of [0, 2%], (2%, 3%], (3%, 5%], (5%, 10%], or (10%, 20%] were 5.1%, 5.1%, 5.1%, 16.5%, and 49.4%, respectively. The percentage of counties showing a larger fluctuation (BR > 20%) has risen to 19.0%, and the fluctuation coefficient has increased in 64.6% of counties.

After 2010, the fluctuation of relative meteorological yield decreased greatly, with just a few counties being higher (Figure 10d). The proportions of counties having average fluctuation coefficients of [0, 2%], (2%, 3%], (3%, 5%], (5%, 10%], and (10%, 20%] are 10.1%, 34.2%, 31.7%, 20.3%, and 2.5%, respectively. Huating and Jingning counties show large fluctuations (BR > 15%). The fluctuations of 87.3% counties have fallen significantly. The regions with severe yield fluctuations have shifted from southern Gansu to western Gansu since 2000.

5.2.4. Spatial Distribution of Different Yield Reduction Rate Probabilities in Gansu Province Counties

The spatial distributions of different yield reduction rate probabilities in counties of Gansu Province are shown in Figure 11.

The probability of a grain yield reduction rate between [−5%, 0] ranged from 5.4% to 51.4%, and the mean probability reached 23.4% (Figure 11a). Counties prone to extremely slight disaster loss include Jingyuan, Qinzhou, Qin’an, Wushan, Minqin, Ganzhou, Gaotai, Suzhou, Jinta, Anxi, Cheng, Hui, Diebu, and Xiahe (P_[−5%,0] > 32.4%). In twenty-two counties, the probability in this loss range is minimal (P_[−5%,0] < 16.2%).

Second, the probability in the [−10%, −5%) interval varied from 0 to 18.9%, and the mean probability reached 9.0% (Figure 11b). Twenty-one counties were prone to slight disasters (P_{[−10%,−5%)} > 13.5%). In Jiayuguan, Qinzhou, Gaotai, Jingning, Suzhou, Huachi, Zhengning, Hui, Zhouqu, and Diebu counties, the probability was small, at only 2.7%.

Third, the probability in the range [−20%, −10%) changed from 0 to 16.2%, and its mean value was 6.4% (Figure 11c). Seventeen counties had an occurrence probability of more than 10.81%, while in 23 counties, the probability was only 2.7%. Additionally, Ganzhou, Anxi, Xifeng, Hui, and Kangle counties have not been shown to suffer from slight–moderate disasters.

Figure 11d depicts the probability of a grain yield reduction rate in the range [−30%, −20%). In total, 62.0% of the counties did not suffer from moderate disasters, and these are mainly distributed in central and western Gansu. The prone counties are primarily distributed in southeastern Gansu Province. The occurrence probability in nine counties exceeded 8.1%.

Counties prone to severe disasters (AR < −30%) are mainly distributed in the Hexi Corridor, such as Jinchang, Yongchang, Liangzhou, Gulang, Ganzhou, Suzhou, Anxi, Subei, Yumen, and Dunhuang, as well as Huining, Huating, and Li in Central Gansu (P_(<−30%) > 8.1%) (Figure 11e). In total, 27.9% of counties have been free of severe and catastrophic disasters, and these are mainly distributed in southwestern Gansu.

5.3. Zoning of Grain Production Risk in Gansu Province

The comprehensive risk of grain production is evaluated by taking into account long-term yield reduction, catastrophe, disaster variation trend, grain yield increase, probability of severe disaster, and other factors (Figure 12). Most counties in Gansu Province belong to medium or medium–lowrisk areas. At the same time, there are fewer high, medium, and low risk areas.

According to the standard deviation grading method, counties with high, medium–high, medium, medium–low, and low risk represented 7.6%, 13.9%, 46.8%, 26.6%, and 5.1%, respectively (Figure 12a). High risk counties include Huating, Huan, Huining, Jinchang, Qingcheng, and Zhangjiachuan. Cheng, Diebu, Jinta, and Xiahe counties are low risk.

In addition, according to the K-means algorithm, counties with high, medium–high, medium, medium–low, and low risk accounted for 2.5%, 16.5%, 45.6%, 27.9%, and 7.6%, respectively (Figure 12b). Only Huating and Jinchang counties were found to be high risk regions, while Cheng, Diebu, Jinta, Xiahe, Gaolan, and Kang counties were low risk.

Regardless of the classification method, Huating and Jinchang counties are designated high risk areas, whereas Cheng, Diebu, Jinta, and Xiahe counties are all identified as low risk areas.

By comparison, in several counties, the risk grade calculated by the K-means clustering algorithm is slightly lower than that determined by the other approach (Figure 13). The risk grades of 11 counties differ, suggesting that the classification method is critical to regional risk judgment.

5.4. Verification of Risk Outcomes of Grain Production

5.4.1. The General Crop Disaster Situation in Gansu Province

The spatiotemporal variations in the total-affected rate and total-disaster rate of crops in Gansu Province are shown in Figure 14.

In the 1980s, the total-affected rate in 86.08% of the counties was between 15% and 60% (Figure 14a). The proportions of counties with a total-affected rate of [0, 15%], (15%, 30%], (30%, 45%], (45%, 60%], and (60%, 100%), were 10.1%, 22.8%, 38.0%, 25.3%, and 3.8%, respectively. The most seriously affected counties were Xifeng, Heshui, and Zhenyuan, with a total-affected rate of more than 60%. By the 1990s, the proportion of seriously affected regions dramatically rose (Figure 14b). County proportions in the above five intervals were 11.3%, 11.3%, 33.8%, 32.5%, and 11.3%, respectively. Furthermore, the total-affected rate increased dramatically in 63.3% of the counties, with Gaotai, Anxi, Hui, Kangle, and Dongxiang counties experiencing an increase of more than 30%. By the 2000s, the affected rate gradually decreased (Figure 14c). The proportions of counties in those intervals were correspondingly 20.0%, 31.3%, 27.5%, 15.0%, and 7.5%, respectively. Huining, Gulang, Tianzhu, Jingning, Huan, and Hui were severely affected by meteorological disasters. The total-affected rates of 70.0% of counties drastically dropped, and five counties showed a decline of more than 30%. Since 2010, the total-affected rate of counties has decreased more noticeably (Figure 14d). The proportions of counties in the five intervals are 51.3%, 32.5%, 12.5%, 2.5%, and 1.3%, respectively. The worst-affected county is Jingning County. The total-affected rate here fell in 86.3% of the counties, and eight counties experienced a drop of more than 30%. Overall, in the past few decades, the proportions of counties with total-affected rates in the intervals [0, 15%], (15%, 30%], (45%, 60%], and (45%, 100%] are 11.3%, 32.5%, 43.8%, 10.0%, and 2.5%, respectively (Figure 14e). Tianzhu and Hui counties are the most seriously afflicted regions (Ratio_tsz > 60%).

Furthermore, in the 1980s, the county proportions with crop total-disaster rates in the [0, 10%], (10%, 20%], (20%, 30%], (30%, 40%], and (40%, 100%] intervals were 10.1%, 15.2%, 29.1%, 20.3%, and 25.3%, respectively (Figure 14f). In the 1990s, disaster-prone areas increased dramatically (Figure 14g). The county proportions with total-disaster rates in the above five intervals were 12.4%, 11.1%, 23.5%, 34.6%, and 18.5%, respectively. The total-disaster rate increased dramatically in 51.9% of counties, with Minqin, Anxi, and Akesai counties experiencing more than 20% increases. By the 2000s, the total-disaster rate had gradually declined (Figure 14h). The county percentages with total-disaster rates in the five intervals are 18.5%, 32.1%, 24.7%, and 12.4%, respectively. The total-disaster rate fell dramatically in 75.3% of counties, with ten counties experiencing a decrease of more than 20%. After 2010, the declining trend of the total-disaster rate became more apparent (Figure 14i). The county percentages of total-disaster rates in these intervals were 58.0%, 24.7%, 8.6%, 7.4%, and 1.2%, respectively. The disaster rate in Dongxiang is the most severe. The total-disaster rate fell greatly in 90.12% of counties, with six counties experiencing a decrease of more than 30%.

Over the past few decades, the proportions of counties with an average annual total-disaster rate of [0, 10%], (10%, 20%], (20%, 30%], (30%, 40%], and (40%, 100%] in Gansu Province are 13.6%, 23.5%, 37.0%, 19.8%, and 6.2%, respectively (Figure 14j). Huining, Tianzhu, Huan, Hui, and Dongxiang counties have been the worst harmed (Ratio_tcz > 40%).

5.4.2. Crop Drought-Disaster Situation in Gansu Province

The drought-affected and drought-disaster rates of crops in Gansu Province were investigated (Figure 15).

In the 1980s, the proportions of counties with drought-affected crop rates of [0, 7%], (7%, 14%], (14%, 21%], (21%, 28%], and (28%, 100%] were 40.7%, 22.2%, 19.8%, 9.9%, and 7.4%, respectively (Figure 15a). Severe drought-affected areas included Yongdeng, Jingyuan, Gulang, Akesai, Qingcheng, and Huan (Ratio_ghsz > 28%). By the 1990s, drought-affected areas had greatly increased (Figure 15b). In these five intervals, the county proportions were 16.1%, 9.9%, 13.6%, 14.8%, and 45.7%, respectively. The drought-affected rate exceeded 28% in 45.7% of the counties, and the drought situation became relatively poor. In addition to this, drought-affected rates rose in 86.4% of counties, with nine counties showing an increase of more than 30%. By the 2000s, drought-affected rates had gradually declined (Figure 15c). The proportions of counties in these intervals were 32.1%, 23.5%, 16.1%, 8.6%, and 19.8%, respectively. The drought-affected rate fell in 81.5% of the counties, and Jingning, Suzhou, and Akesai counties saw more than 30% reductions. After 2010, the drought-affected rate showed a more pronounced downward trend (Figure 15d). The county proportions in five intervals were 55.6%, 24.7%, 8.6%, 8.6%, and 2.5%, respectively. Jingtai and Jingning were the worst hit by drought. The drought-affected rate fell in 87.7% of the counties, with Huining, Gulang, and Cheng experiencing a decrease of more than 30%. On the whole, during the past few decades, drought has seriously afflicted Yongdeng, Baiyin, Jingyuan, Huining, Jingtai, Gangu, Gulang, Tianzhu, Shandan, Jingning, Huan, Longxi, Weiyuan, Hui, and Dongxiang (Ratio_ghsz > 28%) (Figure 15e).

Moreover, the variations in drought-disaster rates were analyzed. In the 1990s, the proportions of counties with drought-disaster rates of [0, 7%], (7%, 14%], (14%, 21%], (21%, 28%], and (28%, 100%] were 22.2%, 11.1%, 17.3%, 25.9%, and 23.5%, respectively (Figure 15f). By the 2000s, drought-disaster rates in all counties had gradually declined (Figure 15g). County proportions in these intervals were 44.4%, 19.8%, 17.3%, 7.4%, and 11.1%, respectively. The drought-disaster rate dropped dramatically in 81.5% of the counties, with nine counties showing decreases of more than 20%. After 2010, the drought-disaster rate in Gansu Province counties declined considerably, and was no more than 21% (Figure 15h). Proportions of counties in the intervals of [0, 7%], (7%, 14%], and (14%, 21%] were 75.3%, 14.8%, and 9.9%, respectively. The drought-disaster rate decreased in 92.6% of the counties, with Huining, Gulang, and Xihe counties experiencing drops of over 30%. From 1984 to 2020, the county proportions of the above five intervals were 30.9%, 25.9%, 21.0%, 17.3%, and 4.9%, respectively (Figure 15i). Huining, Gulang, Hui, and Dongxiang counties suffered severe drought (Ratio_ghcz > 28%).

5.4.3. Verification of Grain Comprehensive Risk in Gansu Province

The crop disaster situation was utilized to validate the grain production risk. The correlations between risk indicators and crop disaster situations are displayed in

Table 3. Spearman’s correlation coefficients between risk indicators and disaster conditions (* and ** show statistically significant correlation (p < 0.05) and extremely significant correlation (p < 0.01), respectively. ^a denotes reaching the threshold for significance after Bonferroni correction (p < 0.0002)).

Risk Indicators	Total-Affected Area		Ratiotsz	Total-Disaster Area		Ratiotcz	Drought-Affected Area		Ratioghsz	Drought-Disaster Area		Ratioghcz
	Crop	Grain		Crop	Grain		Crop	Grain		Crop	Grain
Yts	−0.06	−0.03	−0.02	−0.06	−0.03	−0.02	−0.04	−0.03	−0.03	−0.05	−0.03	−0.01
AR	0.20	0.25 *	0.24 *	0.21	0.26 *	0.24 *	0.22	0.25 *	0.28 *	0.22	0.27 *	0.25 *
MR	0.15	0.19	0.19	0.14	0.18	0.16	0.13	0.16	0.15	0.13	0.17	0.15
BRs	−0.32 **	−0.27 *	−0.17	−0.34 **	−0.29 **	−0.21	−0.33 **	−0.28 *	−0.22 *	−0.34 **	−0.27 *	−0.23 *
BR	0.25 *	0.31 **	0.27 *	0.26 *	0.32 **	0.28 *	0.26 *	0.30 **	0.30 **	0.26 *	0.32 **	0.28 *
CVY	0.49 **a	0.50 **a	0.44 **a	0.51 **a	0.52 **a	0.45 **a	0.49 **a	0.50 **a	0.47 **a	0.50 **a	0.52 **a	0.46 **a
CVYR	−0.08	−0.05	0.01	−0.09	−0.07	−0.04	−0.08	−0.07	−0.05	−0.09	−0.06	−0.05
AR in the 1980s	0.30 **	0.30 **	0.23 *	0.32 **	0.32 **	0.26 *	0.31 **	0.31 **	0.27 *	0.32 **	0.30 **	0.27 *
AR in the 1990s	0.43 **a	0.39 **a	0.36 **	0.45 **a	0.40 **a	0.36 **	0.45 **a	0.41 **a	0.42 **a	0.45 **a	0.40 **a	0.39 **a
AR in the2000s	−0.05	0.02	0.05	−0.05	0.02	0.04	−0.06	−0.01	0.03	−0.06	0.02	0.02
AR in the 2010s	−0.15	−0.17	−0.11	−0.16	−0.19	−0.14	−0.15	−0.16	−0.10	−0.15	−0.17	−0.13
BR in the 1980s	0.32 **	0.31 **	0.21	0.34 **	0.34 **	0.25 *	0.32 **	0.30 **	0.24 *	0.32 **	0.30 **	0.24 *
BR in the 1990s	0.45 **a	0.41 **a	0.37 **	0.46 **a	0.42 **a	0.38 **a	0.47 **a	0.43 **a	0.43 **a	0.47 **a	0.42 **a	0.41 **a
BR in the 2000s	−0.04	0.05	0.03	−0.04	0.05	0.03	−0.06	0.011	−0.01	−0.05	0.04	0.00
BR in the2010s	−0.15	−0.19	−0.10	−0.16	−0.20	−0.12	−0.16	−0.18	−0.10	−0.16	−0.19	−0.12
P[−5%,0]	0.15	0.15	0.11	0.17	0.17	0.15	0.17	0.17	0.20	0.18	0.18	0.17
P[−10%,−5%)	0.02	0.05	0.04	0.01	0.04	0.01	0.03	0.05	0.02	0.01	0.05	0.01
P(<−30%)	−0.11	−0.06	−0.17	−0.12	−0.07	−0.20	−0.12	−0.10	−0.19	−0.13	−0.10	−0.20
Comprehensive risk level	0.20	0.26 *	0.25 *	0.20	0.27 *	0.23 *	0.21	0.26 *	0.26 *	0.21	0.27 *	0.24 *

. In this case, the risk indicators took standardized values, i.e., the greater the value of each indicator, the higher the risk.

As expected, disaster information positively correlated with most risk indicators and comprehensive risk levels, suggesting that risk outcomes were generally reliable.

Among them, BR, CV_Y and AR in the 1980s and 1990s, BR in the 1980s and 1990s, and the comprehensive risk level significantly positively correlated with crop disaster conditions, while the correlation was negative for BR_s.

Secondly, the correlation between the risk indicators and the drought-disaster condition was comparable to that of the total disaster condition, indicating that drought hazard was the primary cause of grain yield reduction and agricultural production risk in Gansu Province.

In contrast, the correlation was more significant in the 1980s and 1990s, showing that the severity of disaster losses during those periods profoundly influenced the county’s overall risk.

Furthermore, even after Bonferroni correction for the significance level (p < 0.0002), CV_Y, as well as AR and BR in the 1990s, still significantly positively correlated with disaster information, illustrating that yield fluctuations had great influence on the scope and severity of grain disaster. Additionally, the yield loss and instability in the 1990s also contributed greatly to the disaster situation in this county. Additionally, several risk indicators did not pass the Bonferroni significance threshold (p < 0.0002). This may be because the Bonferroni correction was overly strict, and there was still plenty of room to improve the risk evaluation index and methods.

6. Discussion

Agrometeorological disasters have grown more frequent in recent years, damaging crop productivity and quality and severely threatening China’s agricultural production and food security. Therefore, it is important to carry out a disaster risk assessment. Through risk analysis, we can provide essential policy advice for the government in disaster prevention. After weighing the benefits and drawbacks of various assessment methods, a fusion method combining probability statistics and an index system is adopted to conduct a refined assessment of grain production risk at the county level in Gansu Province.

Gansu Province’s risk distribution was highly fragmented, with major regional variations in risk even within a single district. For instance, a district may be regarded as low risk, but a specific county inside that district may be identified as high risk. Previous studies in China have focused primarily on risk assessments at the national [36], provincial [37,38], or district [39,40] levels, but our findings prove the need to undertake refined risk analysis at a smaller administrative scale (county or town), and may also help the government establish county-specific disaster-preventive strategies.

The validation results reveal that drought was the primary cause of disaster loss in Gansu Province, consistent with Wang’s and Chen’s conclusions [30,41]. They found that drought risks were more significant than other agrometeorological hazards and were rising. However, their findings lack in-depth analyses of more minor scales in Gansu Province, or are primarily applicable to specific crops in other provinces.

Furthermore, the initial risk analysis on yield disaster loss only employed a few indicators, while its time series features, such as frequency, intensity, and trend, have seldom been examined [29]. Here, all aspects of grain output variation are addressed, offering complete information for grain production risk management in Gansu Province.

Most regions fall in the low or medium–low risk zone, which is consistent with Hao et al. [42], who concluded that the low risk area of agriculture drought in China was primarily located in the west, and that severe disaster occurrence decreased in most of China. It is also consistent with Blauhut’s outcomes [43], who summarized that China is mostly at low to medium risk of drought. Additionally, the high risk area was primarily concentrated in the east–central part of Gansu Province, whereas western and northern Gansu were in the low risk area, similar to the drought risk distribution identified by He et al., except for the Longnan area [36].

Future risk studies must better grasp geographical and temporal dynamics of risk [43], which is rarely addressed in past research. We employed interdecadal analysis to illustrate the changes in grain production risk, which may give some evidence for the future impacts of climate change on grain production risk [44]. According to our research, risk zones may shift over time. Some high risk places may turn into low risk areas, and vice versa.

Wuwei District contained most risk results, and risk levels to the east and west of Wuwei differ, in accordance with the distribution of climate and natural areas. The counties to the east of Wuwei are mostly rain-fed, and weather conditions significantly influence agricultural production. In the irrigated agriculture regions west of Wuwei, crop growth is less affected by weather factors. In other words, the risk reduction here was highly connected with the irrigated area [45]. Building irrigation infrastructure and guaranteeing a consistent irrigation water supply are critical steps.

In this work, we tried to validate our risk results, and demonstrated the statistically significant correlations between risk and disaster information, indirectly proving its reliability. Moreover, the significance level was adjusted using Bonferroni’s method owing to numerous correlations. However, some correlations failed the significance test after the correction. On the one hand, the Bonferroni correction method is too stringent. When the number of comparisons is high (e.g., more than ten), the significance test level after correction can be too small, resulting in conservative conclusions [46,47,48,49]. Therefore, we marked the significance results before and after correction as a reference. On the other hand, risk was found to be quite complicated, and its evaluation technology still needs to be improved according to the situation [43]. In general, we have made beneficial steps towards the validation of risk evaluation results.

Finally, based on the present state of meteorological disaster risk studies in Gansu Province, we will conduct two additional studies in the future. To thoroughly investigate a single disaster’s effect on agriculture, we will use the disaster stress index [41] and a geographic detector to differentiate the causes of disaster loss. On the other hand, previous studies mostly offered an overall risk map using historical data [50], which fell within the category of static risk assessment. Essentially, the risk must consider the probability of future disaster events and the uncertainty of losses. Especially in the context of climate change, extreme temperature events will become more frequent in most parts of China, and yield losses of main crops will reach 10% to 30%, with spatial heterogeneity becoming considerable [51,52]. Consequently, it is necessary to perform meteorological disaster risk analyses under future climate change scenarios [53,54,55]. The crop growth model can estimate agricultural losses under various natural disaster and climatic scenarios [19,56]. Therefore, we will use the crop and climate model to analyze the development of agrometeorological disaster risk and give scientific advice regarding disaster mitigation efforts.

7. Conclusions

The spatial–temporal distribution characteristics of grain production risk in the districts and counties of Gansu Province were investigated by merging the probability statistics with an index system method and using a long series of historical yield data.

From a district-level perspective, the grain trend yield in districts of Gansu Province exhibits an increasing tendency. Most districts’ average yield reduction rate was less than 10%. In districts other than Lanzhou, Wuwei, Zhangye, Jiuquan, and Gannan, the maximum yield reduction rate exceeded 20%. The average fluctuation coefficient, yield variation coefficient, variation coefficient of yield reduction rate, and fluctuation tendency rate ranged from 3.0% to 8.5%, 0.14 to 0.34, −1.72 to −0.65, and −0.23%/year to 0.34%/year, respectively. In the 1980s, 1990s, 2000s, and 2010s, the average grain yield reduction rates for Gansu Province were 5.5%, 6.6%, 8.1%, and 4.2%, and the average fluctuation coefficients were 5.0%, 5.5%, 7.1%, and 3.8%, respectively. After 2010, the yield reduction in most districts decreased dramatically. Jiayuguan and Jinchang Districts are susceptible to severe disasters.

There are large disparities in the risk level among counties within one district. In most districts, high risk and low risk counties coexist, necessitating a refined risk assessment on a smaller administrative scale. The trend yield in Gansu Province counties is rising. In total, 39.2% of the counties have a positive fluctuation tendency rate, indicating that grain production is still unstable and heavily influenced by meteorological elements. From the 1980s to the 2000s, the yield reduction rate continued to increase, and severe disaster zones greatly widened and shifted, while disaster losses improved significantly after 2010. Counties prone to severe disasters are primarily concentrated in the Hexi Corridor, but 27.85% of the counties were spared from severe disasters, primarily in southwestern Gansu Province. Obviously, food security in Gansu Province has been severe for a long time. Still, in the last ten years, grain yield losses have decreased dramatically, and agricultural disaster resistance abilities have gradually risen.

Most counties in Gansu Province generally belong to medium risk or medium–low risk regions. Huating and Jinchang counties are designated high risk locations, whereas Cheng, Diebu, Jinta, and Xiahe counties are low risk zones. Additionally, risk grade classification is critical for deciding regional risk.

Furthermore, the verification process has indicated that the comprehensive risk level is relatively trustworthy, and drought is the primary cause of the grain yield decline in Gansu Province.

Our analysis at the county level allowed a refined assessment of the grain production risk in Gansu Province. In high risk areas, disaster-preventive capabilities should be improved. The frequent occurrence period of climatic disasters might be avoided by altering the sowing date. Adjusting the crop planting structure, reducing the crop area exposed to weather disasters, and providing agricultural production guidance are important to reducing risks.

In addition, our risk assessment scheme mainly applies to long-series data, which have some limitations. In addition, the refinement of risk outcomes primarily depends on the spatial resolution of historical statistical data, while the data were collected only at the county level and above. Thus, this approach is not applicable at the township and village levels, as well as for more detailed risk zoning. Therefore, by fusing high-resolution (kilometer- or even meter-level resolution) satellite remote sensing information, high-precision disaster data can be rebuilt, and more precise crop information can be obtained, which will expand the application scope of this method.